If you were to look at the PROS and CONS of each I would have to say that the single handed backhand wins hands down.

The single handed backhand provides a greater range of movement in relation to your back swing and follow through. Which means more power in executing your shot and allowing the body to be balanced ready for the next shot. The other point is, that the single handed backhand is a more natural stroke, even compared to the forehand. The reason being that the backhand is played just in front of the forward shoulder and your head is closer to the point of impact.

The two handed backhand is excellent for beginner's who do not have the power in their wrists to properly execute the stroke. Besides if you get used to the two handed backhand it makes it more difficult to master the slice backhand and drop shot!

I disagree with Nathan, there are some pros to the 1 hander........reach and it looks beautiful when it comes off.

I think the versatility of the 2 handed backhand wins hands down.
I use a 1 handed bh cos it works for me, but its hard to hit high balls, you have to prepare yourself earlier to execute your shot, its harder to hit off balance, 2 hander has same amount of power with less effort.................

I used to hit with both types of backhands at the beginning. I noticed I was stronger with one handed and at the time I loved hitting with slice. My 2 hander was not too strong, maybe only down the line, but I can do that now with my one hander. So today I play with a 1 handed backhand that has a mean topspin or slice.

It Doesn't Matter. It is who ever wins. That's the backhand you should be using. Mine is a single and a Double I win.
Pro: single Reach. Faster to learn volleys and Slice. Power Through Leverage. Con Single Must hit closed Stance most of the time.
Pro: Double Handed Backhands can be hit off of either foot/balance. IT can generate same power as a single in a smaller Swing. Con no reach, May make it harder for a player to develop a slice, Backhand Overhead and Volleys. most people are not coordinated with their left hand.
Think about womens Tennis. How many Serve and Volley-ers have double handed back hands.
Mens Tennis, Jim Courior and Andy Roddick have bad volleys